230 ON THE TOTAL INTENSITY OF INTERFERING LIGHT. A similar formula holds good for q, whence D2I= limit of Let now 2?r (#' — x) -----1_------i. = Q.U) whence ^ , 7 dx = -=-— du, A7T and the limits of u are ultimately — oo aud + °o , since a ultimately vanishes. Hence .. . f imit Of J du A similar formula holds good for y, and we have, therefore, if A be the whole area of the aperture or apertures. Now / ought to be equal to A, and, therefore, D = b\. CASE II. Aperture in front of a screen. The formula for the illumination is given iu Airy's Tract, Art. 73. We have as before, = limit of jjjjjj*****1 cos j^"^- [^ - & + 2/"J - f] ~ y>dx dy dx'dy'